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16.1/2 points Previous AnswersTanApCalc9 11.2.035_Determine the convergence or divergence of the sequence {a}Vn + 5convergesdivergesIf the sequence converges find i...

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16.1/2 points Previous AnswersTanApCalc9 11.2.035_Determine the convergence or divergence of the sequence {a}Vn + 5convergesdivergesIf the sequence converges find its limit: (If an answer does not exist; enter DNE:)~1Need Help?Read It_Talk to_ Tutor

16. 1/2 points Previous Answers TanApCalc9 11.2.035_ Determine the convergence or divergence of the sequence {a} Vn + 5 converges diverges If the sequence converges find its limit: (If an answer does not exist; enter DNE:) ~1 Need Help? Read It_ Talk to_ Tutor



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In Problems $5-14$, use the Comparison Tests for Convergence or Divergence to determine whether each series converges or diverges. $$ \sum_{k=1}^{\infty} \frac{6}{5 k-2} $$

Isn't here Harrison test whether the serious converges or diverges call this is a pen. So then from here, so they have to So it got her Summation of. So I'm going to compare that to 3/2. Okay. 2 3/2. So it's going to be our this event. Okay? So let's go ahead and apply that to limit has and approaches infinity the cube root have an accurate three three times radical and plus two or two and squared plus five Divided by 3/2 Instead of 3/2. All right. So now Simplifying this out here at the 3/2 and three over to cancel out here. So then we have And to the 1/2 Times instead of 3/2. It's two and 2 three or 2 Out of my and squared plus five. Any of those exponents there gives us the limit as n approaches infinity of n squared plus two and 3/2 writing by hand squared plus five. So it's equal to one. So either both coverages are both their riches, but we know that the 3/2 to the Okay three or 2 power here. So this converges by P series since 3/2 is greater than one, that's P. So therefore both coverage.

The comparison tests to determine with this series converges or diverges and celebrate. Take this or a So then I'm going to compare that to you 3/2 kids and a 3/2. Just as I know you know that this converges not to be serious. That basically makes Because P is equal to 3/2 which is greater than one. Okay, so it's going to be our be so bad. Let's take the limit as and approaches infinity of three radical and plus 2/2 and squared plus five founded by 3/2 and 3/2. And I'm going to multiply by the reciprocal here which ends up multiplying these two sets. So on top we got six and squared Plus four and the 3/2 on the bottom we get six in squared plus 15. Take an open that has an approaches infinity here, that equals one. And since we know that one of these series converges then they're both good good perch.

Comparisons has to determine if this serious coverages for diverges compare that to five over read to the cake. That's going to be RPS so bad. You know that that by the geometric series convergence since one third system one, It's 1/3 to the Cape. And so then we take the limit as and approaches infinity Of 5/3 to the end. Plus two. Try to buy 5/3 to the end. Simplifying that out here, we get the limit has and approaches infinity of five times 3 to the 4th power. Try to buy five times 3 to the n plus 10 equals one. Therefore, since we know that one of them converges, both can approach.

Test see if the series converges or diverges the corpus case event Compare that to one over radical cake call that piece I've been here. So therefore we take the limit as N approaches infinity here Of screwed event over and plus four. I want to buy one over squared of it. Simplifying this out here. I got the limit past and approaches infinity of And over and plus four since the radical end. Well here I'll just do it this way. So then the radical and Radical and gives us an overhand plus war And so then it's gonna equal one. So either both coverages were both coverages and so but we know that one of the radical end That type urges since P is equal to 1/2 Just less than one. So it diverges by P series so therefore both day average.


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